\documentclass[12pt]{article} 
 \textheight15cm \textwidth11cm \parindent0mm \parskip 1ex plus2ex minus0.8ex
\begin{document}
\newtheorem{guess}{Conjecture}
Conjectures are numbered consecutively from the beginning of the document.
\begin{guess}\label{l1} Conjecture \ref{l2} is true  \end{guess}
\begin{guess}\label{l2} Conjecture \ref{l1} is false \end{guess}


\newtheorem{axiom}{Axiom}[section]
\section{A new section}
\begin{axiom} All axioms are very dull \end{axiom}
\begin{axiom} Really, all axioms are very dull \end{axiom}
\section{A new section again}
\begin{axiom} Almost all axioms are very dull \end{axiom}
\end{document}
